# The position of an object moving along a line is given by p(t) = 3t - sin(( pi )/6t) . What is the speed of the object at t = 2 ?

Aug 30, 2017

The speed is $= 2.74 m {s}^{-} 1$

#### Explanation:

The position of the the object is given by the equation

$p \left(t\right) = 3 t - \sin \left(\frac{1}{6} \pi t\right)$

The speed is the derivative of the position

$v \left(t\right) = \frac{\mathrm{dp}}{\mathrm{dt}} = 3 - \frac{1}{6} \pi \cos \left(\frac{1}{6} \pi t\right)$

When $t = 2$

$v \left(t\right) = 3 - \frac{1}{6} \pi \cos \left(\frac{1}{6} \pi \cdot 2\right)$

$= 3 - \frac{1}{6} \pi \cos \left(\frac{1}{3} \pi\right)$

$= 3 - \frac{1}{6} \pi \cdot \frac{1}{2}$

$= 2.74$